Question

the vertices of a quadrilateral in the coordinate plane are known. how can the perimeter of the figure be found?
use the distance formula to find the length of each side, and then add the lengths.
use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.
use the distance formula to find the length of the sides, and then multiply two of the side lengths.

Explanation:

To find the perimeter of a quadrilateral with known vertices in the coordinate plane, we need the lengths of all its sides. The distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) is used to find the length between two points (vertices), which gives the length of a side. Perimeter is the sum of all side lengths, so we find each side's length using the distance formula and then add them. The other options involve slope (for parallel/perpendicular, not length) or multiplying (for area, not perimeter).

Answer:

A. Use the distance formula to find the length of each side, and then add the lengths.